When French luxury goods firm Hermès threw down the gauntlet – a hand-stitched top-grain leather one, of course – to rival Louis Vuitton Moët Hennessy in 2010, it might have been hoping for a discreet, gentlemanly outcome. Instead, the challenge sparked years of public squabbling that in the refined circles inhabited by its wealthy clients could be defined as most ungenteel. Now, having raged for three years, the Gallic "handbag war" is entering a new phase.

Or has Hermès, anxious to remain family-run and independent, engaged in a snobbish and condescending "slander and smear" campaign against its bigger, brasher rival? If so, the company that referred to LVMH boss Bernard Arnault, France's richest man, as an "intruder in the garden" (adding "we don't want him in the house") will have to learn to live with its uninvited and unwanted guest.

If the buoyant luxury goods market, which appears to be bucking the recession, was not so important to France's struggling economy, the handbags-at-dawn standoff between two of the country's most prestigious brands might be mildly amusing.

Its first customer may have been a horse, but Hermès has come a long way from its relatively humble beginnings as a harness and bridle shop for European nobles. This is the company that made scarves for Queen Elizabeth II and Jackie Onassis– who decorated her walls with them – and boots for the former shah of Iran, and created the once-ubiquitous "Kelly" bag, named for Princess Grace of Monaco.

Hermès, which has gone from strength to strength in recent years, and posted a record-breaking profit of €740m in 2012, on a €3.48bn turnover, is also purveyor of the ultimate "it" bag, the Birkin – named after British singer Jane Birkin – whose price can match that of a luxury car and whose exclusiveness has survived reports that queen of bling Victoria Beckham has 100 of them in her closet.

Not that Hermès talks about its customers. For a firm that considers its hand-stitched, hand-crafted goods the ne plus ultra of refinement, good taste and timeless luxury, such a lack of discretion would be downright vulgar. Hermès makes no secret of considering itself several cuts above Louis Vuitton. The right-of-centre Le Figaro newspaper reported that the Hermès family has "always had a condescending view of Louis Vuitton and its bags of coated canvas".

Asked once why Hermès shunned initials, Xavier Guerrand-Hermès, great-great-grandson of Thierry Hermès, who opened the first harness shop in Paris in 1837, retorted: "If someone knows us, they will know us."

To the Hermès clan, LVMH is a brash upstart, as is Arnault, a close friend of former president Nicolas Sarkozy, also viewed as a parvenu. The stable of firms in Arnault's empire, acquired often by snapping up small, dispute-riven companies, includes Moët & Chandon, the world's largest champagne house, as well as Givenchy, Guerlain, Marc Jacobs and Céline.

In 2010, when the French stock-market watchdog, the AMF, announced its investigation into how Arnault acquired his 17% of Hermès shares, it warned it would be "long, difficult and very complex". The inquiry has sparked three years of claims and counter-claims between the luxury giants.

A leaked AMF report carried in Le Monde claimed LVMH, which has since built up its holding to 22.6%, had been increasing its stake in Hermès since 2001 through subsidiaries using the code name Mercure, investing amounts too small to require disclosure. LVMH said it would "vigorously" contest the claims.

Thomas, who will hand over the reins to Axel Dumas, 42, a sixth-generation member of the Hermès family, told French news channel BFMTV: "We must not have someone who is a rival and perhaps a threat holding too-significant capital. From the beginning we have said that the way that LVMH got into Hermès is, and I'm measuring my words, illicit." Thomas has even suggested that LVMH's withdrawal from Hermès is "in the interests of France".

LVMH has repeatedly argued that its actions were perfectly legal. Vice-president Pierre Godé said: "It is not for a publicly listed company to ask whether it likes its shareholders or not. LVMH is a shareholder and asks to be treated like any other."